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cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2...

`cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2`

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To prove the equation \[ \frac{\cos(2A)}{a^2} - \frac{\cos(2B)}{b^2} = \frac{1}{a^2} - \frac{1}{b^2} \] where \( A \) and \( B \) are angles of a triangle, we will follow these steps: ...
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In any DeltaABC , prove that (cos2A)/a^(2)-(cos2B)/b^(2)=(1/a^(2)-1/b^(2))

In A B C Prove that cos^2A/2+cos^2B/2+cos^2C/2lt=9/4dot In cos^2A/2+cos^2B/2+cos^2C/2=y(x^2+1/(x^2)) then find the maximum value of ydot

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In any Delta ABC, prove that :(1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^(2)+b^(2))/(a^(2)+c^(2))

In any triangle ABC, prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^(2)+b^(2))/(a^(2)+c^(2))

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If f(x)sin x cos xdx=(1)/(2(b^(2)-a^(2)))ln f(x)+c, then f(x) is equal to (1)/(a^(2)sin^(2)x+b^(2)cos^(2)x)(b)(1)/(a^(2)sin^(2)x-b^(2)cos^(2)x+b^(2)cos^(2)x+b^(2)cos^(2)x)(d)(1)/(a^(2)cos^(2)x-b^(2)cos^(2)x)

In DeltaABC , prove that: sin^(2)A+sin^(2)B+sin^(2)C =1-cos^(2)A+sin^(2)B+1-cos^(2)C =2-cos(A+B)cos(A-B)-cos^(2)C =2-cos(180^(@)-C)cos(A-B)-cosC.coc{180^(@)-(A+B)} =2+cosC.cos(A-B)+cos(A+B)] =2+cosC.2cosAcosB =RHS Hence proved.

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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. a(cosC-cosB)=2(b-c)cos^2A/2

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  2. a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .

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  3. cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2

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  4. In a Delta A B C ,\ if\ a=2,\ b=3\ a n d\ sin A=2/3 then find /B

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  5. In any triangle A B C , prove that: (sin(B-C))/(sin(B+C))=(b^2-c^2)/(a...

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  6. In any triangle A B C , prove that: \ asin(B-C)+b s in(C-A)+csin(A-B)=...

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  7. In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A...

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  8. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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  9. In any triangle A B C , prove that: (b-c)/(b+c)=(tan((B-C)/2))/(tan((B...

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  10. In any triangle A B C , prove that: acos((B+C)/2)=(b+c)sinA/2

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  11. A tree stands vertically on a hill side which makes an angle of 15^0 w...

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  12. A person, standing on the bank of a river, observes that the angle sub...

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  13. The angle of elevation of to be top point P of the vertical tower PQ o...

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  14. The elevation of a tower at a station A due North of it is alpha and ...

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  15. If in a Delta A B C ,\ /A=45^0,\ /B=60^0,\ a n d\ /C=75^0 , find the ...

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  16. If in any Delta A B C ,\ /C=105^0,/B=45^0, a=2, then find bdot

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  17. In Delta A B C ,\ if\ a=18 ,\ b=24\ a n d\ c=30\ a n d\ /C=90^0 find ...

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  18. In any triangle A B C , prove that following : (a-b)/(a+b)=(tan((A-B)/...

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  19. In any triangle A B C , prove that following : (a-b)cos(C/2) = csin((A...

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  20. In any triangle A B C , prove that following : c/(a-b)=(tan(A/2)+tan(B...

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